Apparatus, system and method to account for spherical aberration at the iris plane in the design of an intraocular lens

ABSTRACT

The present invention includes at least an intraocular lens, and a system and method of customizing at least one characteristic for an intraocular lens, in accordance with a regression that indicates the postoperative spherical aberration at the iris plane of a patient aphakic eye, in order to obtain a desired postoperative condition. The lens, system and method of customizing at least one characteristic of an intraocular lens may include measuring at least one biometric parameter of an eye at a desired light level, determining a desired postoperative condition of the eye, obtaining a corneal spherical aberration and an anterior chamber depth of the eye, and empirically calculating a spherical aberration at an iris or pupil plane of the eye, based on a regression formula comprising at least the corneal spherical aberration and the anterior chamber depth, and cross products thereof.

CROSS-REFERENCES TO RELATED APPLICATIONS

This patent application is a divisional of and claims priority to U.S.patent application Ser. No. 13/651,611 filed on Oct. 15, 2012, whichclaims priority to U.S. provisional patent application 61/547,454 filedon Oct. 14, 2011 and U.S. provisional patent application 61/642,649filed on May 4, 2012, the entire contents of both of which areincorporated herein by reference for all purposes as if fully set forthherein.

FIELD OF THE INVENTION

The present invention relates generally to the design of intraocularlenses (IOLs) and, more particularly, is directed to an apparatus,system and method to account for spherical aberration at the iris planein the design and selection of an intraocular lens.

BACKGROUND OF THE INVENTION

Intraocular Lenses (IOLs) are frequently used for restoring or improvingvisual performance, such as after cataract surgery. Because an IOL maybe selected from various providers and with differing IOLcharacteristics, reliable systems and methods to select IOLs having IOLcharacteristics that achieve the desired refractive outcome for apatient, such as in terms of spectacle correction and/or image quality,are needed. More particularly, it is typically desirable to select anIOL that will substantially achieve emmetropia for the patient aftersurgery, independent of the refractive state of the patient prior toimplantation. The term emmetropia, and variations thereof, is usedherein to indicate a state of vision in which an object at infinitedistance from the subject eye is in sharp focus with the eye's lens in aneutral state.

The IOL characteristics necessary to achieve emmetropia are oftencalculated using empirical regressions. For example, the Saunders,Retzlaff, and Kraff formula (SRK) is a regression formula empiricallyderived from clinical data to indicate the optimal power for an IOL. TheSRK regression formula is:

P=A−2.5*AXL−0.9*K

where P is the IOL power, A is the lens constant, AXL is the axiallength in millimeters, and K is the average corneal curvature indiopters. Unfortunately, the SRK regression formula may yield inadequateindications, which has led to the development of the SRKII and SRK/Tformulae.

More particularly, in the SRK/T method, the calculation is partiallybased on a previous regression analysis to predict the position of theIOL in the eye after surgery. Once the position is known, the IOL powerto implant is calculated by simple paraxial optics, taking into accountthat the eye is a two lens system (wherein the two lenses are the corneaand the IOL), focusing on the retina. This approach is based onFyodorov's theoretical formula.

There are numerous other formulae for calculating IOL characteristics,such as the Haigis, Hoffer Q, Olsen, and Holladay 1 and 2 models, forexample. An in-depth analysis of IOL power calculation methods isprovided in Shammas H J (ed.), Intraocular Lens Power Calculations,Thorofare, N.J.; Slack (2004).

Current power calculation procedures are paraxial and by definition donot account for spherical aberration present in cornea and IOL. Raytracing procedures include wavefront aberrations but this is not acommon tool in current clinical practice.

Various IOLs are designed to correct for either no corneal sphericalaberration, or, at best, for the average corneal spherical aberration,present in a cataract population. Further, these IOL lenses, whetherdesigned to correct for no corneal spherical aberration or the averagecorneal spherical aberration, are typically designed based solely on theaverage distance between the cornea and the implanted IOL. However, itis well understood that, in a typical sample of patients, the cornealspherical aberration may vary well outside the average range, as may thedistance between the cornea and the IOL upon implantation. Thesevariations may occur, for example, due to the patient's preoperativestate, due to the surgical precision, or due to the healing processlikely for a given eye configuration, for example. Available lensestypically do not provide post-operative spherical aberrationcompensation for patients having non-average eye characteristics priorto implantation. Since the wavefront aberrations change as a wavefrontpropagates through the eye, a procedure to predict the sphericalaberration at the pupil plane creates the possibility to design and toselect an IOL to obtain a desired ocular spherical aberration.

Post-lasik eyes are a particular example of eyes that are not “average”.For example, the post-lasik eye may have characteristics that aredifficult to measure due to the surgical modifications to the eye, andit is well understood that these surgical modifications to thepost-lasik eye, such as the decoupling that occurs between the anteriorand posterior corneal radius after lasik, make certain of the eyecharacteristics calculated for “average” patients inaccurate forpostlasik eyes. Thus, it is well known that it is exceedingly difficultto provide a recommended IOL having characteristics that will producethe desired refractive outcome and residual ocular spherical aberrationfor post-lasik patients.

More particularly, for example, it has been widely reported thatstandard lasik procedure may typically generate large amounts of cornealaberrations. This may be inferred because post-lasik patients typicallypresent higher amounts of corneal aberrations, likely due to the lasiksurgery, than would an “average” patient. Such aberrations should not beexcluded in the calculation of recommended IOL characteristics if thedesired refractive outcome is to be obtained.

Thus, the need exists for an apparatus, system and method forrecommending an IOL having characteristics likely to provide an improvedvisual outcome by accounting for at least the post-operative sphericalaberration at the iris plane and that is simpler than ray tracing. Thisneed may be met, for example, by accounting for a particular patient'sexpected anterior chamber depth (ACD), and more particularly byaccounting for a non-average distance between the cornea and theimplanted IOL, and/or by additionally considering a particular patient'svariation from the average corneal spherical aberration.

BRIEF DESCRIPTION OF THE FIGURES

Embodiments of the present invention will be understood with referenceto the detailed description in conjunction with the accompanyingfigures, in which like numerals indicate like aspects, and wherein:

FIG. 1 is a graphical representation of the elements of an eye modelused in various embodiments of the present invention;

FIG. 2 is a magnified view of the retinal region of the graphicalrepresentation shown in FIG. 1;

FIG. 3 is a flow chart illustrating a method of selecting an IOLaccording to exemplary embodiments of the invention;

FIG. 4 is a bar diagram illustrating, based on an execution of method100 using the MODDE design of experiments, the significance of certainfactors in the spherical aberration response at the iris;

FIG. 5 is a graphical illustration of the predicted aphakic sphericalaberration at the iris plane for a pupil of 5.3 millimeters and ananterior corneal radius of 7 millimeters for different levels of cornealspherical aberration and different post-op ACD distances present in acataract population;

FIG. 6 graphically illustrates the predicted aphakic sphericalaberration at the iris plane for a pupil of 5.3 millimeters and ananterior corneal radius of 7.77 millimeters for different levels ofcorneal spherical aberration and different post-op ACD distances presentin a cataract population;

FIG. 7 illustrates the predicted aphakic spherical aberration at theiris plane for a pupil of 5.3 millimeters and an anterior corneal radiusof 8.5 millimeters for different levels of corneal spherical aberrationand different post-op ACD distances present in a cataract population;

FIG. 8 is a graphical illustration for three different IOLs withdifferent levels of spherical aberration result in different best focusmodulation transfer function results obtained with the present inventionfor an eye having a corneal spherical aberration of 0.17 μm for a 6 mmcorneal aperture;

FIG. 9 is a graphical illustration for three different IOLs withdifferent levels of spherical aberration result in different best focusmodulation transfer function results obtained with the present inventionfor an eye having a corneal spherical aberration of 0.27 μm for a 6 mmcorneal aperture;

FIG. 10 is a graphical illustration for three different IOLs withdifferent levels of spherical aberration result in different best focusmodulation transfer function results obtained with the present inventionfor an eye having a corneal spherical aberration of 0.39 μm for a 6 mmcorneal aperture; and

FIG. 11 is a block diagram illustrating the implementation of thepresent invention in a clinical system.

FIG. 12 illustrates the dependence of spherical aberration with cornealspherical aberration (6 mm) and pupil plane.

FIG. 13 is a graph illustrating R² for measured ocular sphericalaberration versus calculated ocular spherical aberration.

SUMMARY OF THE INVENTION

The present invention includes at least an intraocular lens, and asystem and method of customizing or selecting at least onecharacteristic for an intraocular lens, in accordance with a regressionthat indicates the postoperative spherical aberration at the iris planeof a patient eye, in order to obtain a desired postoperative condition.

The method of customizing at least one characteristic of an intraocularlens may include measuring at least one biometric parameter of an eye ata desired light level, determining a desired postoperative condition ofthe eye, obtaining a corneal spherical aberration and an expectedpost-operative anterior chamber depth of the eye, and calculating aspherical aberration at an iris plane of the eye, based on a modelregression formula comprising at least the corneal spherical aberration,corneal power and the post-operative anterior chamber depth, and crossproducts thereof. The method may further include predictivelyestimating, in accordance with an output of the empirically calculatingand the at least one biometric parameter, the at least onecharacteristic of the intraocular lens to obtain the desiredpostoperative condition.

The at least one biometric parameter may be at least one of axiallength, and corneal power, and the desired light level may be at 6millimeters pupil, for example. The desired postoperative condition maycomprise a postoperative refraction, or the at least one characteristicof the intraocular lens may be an optical power, for example.

In addition to aspects of the aforementioned method, the system forpredicting at least one characteristic of the intraocular lens mayinclude a first computing device capable of measuring at least onebiometric parameter of an eye, a second computing device programmed tosimulate a corneal spherical aberration and a post-operative anteriorchamber depth of the eye according to the at least one biometricparameter, and a third computing device programmed to apply, by at leastone computing processor, a regression to the at least one biometricparameter, the corneal spherical aberration, the post-operative anteriorchamber depth, and cross products thereof, wherein the regression is ofthe form:

SA_(r)=−0.285451+1.00614*SA_(c)+0.0742716*ACD+0.0371122*cor+0.153398*SA_(c)*ACD−0.0788237*SA_(c)*cor−0.00967978*cor*ACD,

wherein SA_(r) is spherical aberration at an iris plane of the aphakiceye, SA_(c) is the corneal spherical aberration, ACD is the anteriorchamber depth, and cor is an anterior corneal radius of the eye.

The system may further include an output from the third computingdevice, comprising an optimized one of the at least one characteristicto obtain a desired postoperative condition calculated in accordancewith the regression. The system may further include a feedback input tothe third computing device for modifying the regression in accordancewith the optimized one of the at least one characteristic.

In addition to the aspects of the method and system of the presentinvention, an intraocular lens according to the present invention mayinclude a selected optic from a plurality of available optics, whereinthe selected optic may be a selection capable of correcting a sphericalaberration at an iris plane of the eye that obeys the equation:

SA_(r) =−A+B*SA_(c) +C*ACD+D*cor+E*SA_(c)*ACD−F*SA_(c)*cor−G*cor*ACD,

wherein A, B, C, D, E, F and G are empirically derived constants, SA_(r)is the spherical aberration at the iris plane, SA_(c) is cornealspherical aberration of the eye, ACD is a predicted post-operativeanterior chamber depth of the eye, and cor is an anterior corneal radiusof the eye. The lens may further include at least one haptic forphysically supporting the selected optic in situ.

Another preferred method comprises fitting the measured ocular SA to themeasured corneal spherical aberration and IOL position or pupil plane.This can be done in order to yield personalized constants.

Therefore, the present invention provides an apparatus, system andmethod an apparatus, system and method for recommending or designing anIOL having characteristics likely to provide an improved visual outcomeby accounting for at least the post-operative spherical aberration atthe iris plane. The present invention accounts for anterior chamberdepth (ACD), and more particularly accounts for the non-average distancebetween the cornea and the implanted IOL, and additionally considersvariations in corneal spherical aberration outside the average range.

DETAILED DESCRIPTION OF THE EMBODIMENTS

It is to be understood that the figures and descriptions of the presentinvention have been simplified to illustrate elements that are relevantfor a clear understanding of the present invention, while eliminating,for the purpose of clarity and brevity, many other elements found intypical implantable optic apparatuses, systems and methods. Those ofordinary skill in the art may thus recognize that other elements and/orsteps are desirable and/or required in implementing the presentinvention. However, because such elements and steps are well known inthe art, and because they do not facilitate a better understanding ofthe present invention, a discussion of such elements and steps is notprovided herein. The details of the present invention are provided withrespect to the figures referenced herein, and further with respect toAppendix A, attached hereto, in which appendices certain additionaldetails of the present invention are provided with reference to thedescription immediately herein below. The disclosure herein is directedto all such variations and modifications to the disclosed elements andmethods known to those skilled in the art.

The present invention is directed to apparatuses, systems and methodsfor selecting characteristics, such as optical power, for spherical andaspheric intraocular lenses (IOLs) to provide a predetermined ocularspherical aberration and/or refractive outcome for “average” and“non-average” patients. Aspects of the invention may be understood withreference to FIG. 1, which is a graphical representation of a model eye20 having cornea 22, iris 24, retina 26, and optical axis 28. IOL 30 isdisposed within eye 20, and IOL 30 may include an optic 32 and one ormore haptics 34 having distal ends 38. In general, eye 20 may have thedimensional parameters illustrated by the geometry shown, including theaxial length (AXL) and the anterior chamber depth (ACD) of eye 20.

As used herein, the anterior chamber is the space between cornea 22 andfront vertex of the IOL. The anterior chamber is filled with the aqueoushumor, and communicates through the pupil with the posterior chamber.The span of the anterior chamber is herein defined as the ACD. Theaverage adult eye has an ACD of about 3.15 mm, although the ACDtypically shallows by about 0.01 mm per year. Further, the ACD isdependent on the accommodative state of the eye, and is indicative ofthe accommodative capability of the eye. The range of ACD may varybetween 2 mm and 5 mm

Other dimensional parameters that may be included in model eye 20include, but are not limited to, the corneal radius (CR), the cornealpower (K) and the crystalline lens thickness (LT). Model eye 20 may alsoinclude various other parameters, such as, for example, the refractiveindices of the various portions of eye 20 and/or IOL 30.

The illustration of FIG. 1 indicates a coordinate system having ahorizontal axis 40 and a vertical axis 42, shown in units ofmillimeters. FIG. 1 shows a plurality of rays 44 entering cornea 22 andIOL 30. The plurality of rays 44 comprises a paraxial ray 50 that isdisposed near the optical axis 28, and a marginal ray 52 that isdisposed near the edge of the opening formed by the iris 24. Theplurality of rays 44 additionally comprises an averaged ray 51 disposedbetween the paraxial ray 50 and the marginal ray 52, for example, at aheight, at the pupil, of 1/{square root over (2)} or ½ times the heightof the entrance pupil height.

Referring now to FIG. 2, shown is a magnified view of the region aroundretina 28, illustrating that rays 50, 51, 52 may come to focus atdifferent points along optical axis 28. These points of focus arelabeled as marginal focus, best focus, and paraxial focus. Asillustrated, the distance between the marginal focus and the best focusmay be used to define a longitudinal spherical aberration (LSA). A LSAmay result, for example, when the surfaces of IOL 30 are spherical,and/or due to a native spherical aberration of the eye, such as acorneal spherical aberration (SA). Alternatively, one or more of thesurfaces of IOL 30 may comprise an aspheric profile that is configuredto reduce or to optimize or to eliminate the spherical aberrationsproduced by IOL 30 or by portions of eye 20, such as the aforementionedSA produced by cornea 22.

The present invention may be used in conjunction with model eye 20 toselect the characteristics of IOL 30 to be implanted into a subject eyeor a class of subject eyes. For example, a class of subject eyes mayinclude subjects of a particular age group or condition (e.g., a classof subjects who have had lasik or a similar procedure). In certainembodiments, measurements from a subject eye, such as the AXL, ACD, SA,CR and/or LT, may be used in conjunction with statistical data and/or ananalytical tool to determine the characteristics of IOL 30. Thecharacteristics of the IOL resulting from embodiments of the inventionmay include the power of the IOL, the thickness of the IOL, theasphericity of the IOL, and/or the location of the IOL within the eye,for example.

The present invention provides a customizable procedure for predictingthe optimum IOL characteristics of a specific IOL 30 for the eye of aparticular individual. The apparatus, system and method discussedherein, in formulating the recommendation of IOL characteristics, maytake into account biometric parameters of the individual patient, suchas the SA and the expected or predicted post-op ACD of the subject eye.The empirical approach discussed herein illustrates that the apparatus,system and method of the present invention are robust for averagepatients, as well as for non-average patients having most levels of SAand most variations in ACD. Such non-average patients may be andinclude, for example, post-lasik patients.

More particularly, in the present invention the residual sphericalaberration in the aphakic eye may be calculated empirically and/or bysimulation, such as based on a number of experimental design factors,and may be used to recommend one or more IOL characteristics, such asIOL spherical aberration level, IOL power or IOL placement. FIG. 3 is aflow diagram illustrating a method 100 in accordance with the presentinvention. Of note, the particular design of experiments in the presentinvention, as indicated by the steps of method 100, was developed andexecuted by the present inventors using the MODDE software program,although other simulations and/or experimental design programs may, ofcourse, be used.

At step 102, the corneal spherical aberration may be measured/simulatedat a particular light level, such as at a light level correspondent to a6 millimeter pupil size, and more particularly, the distance between thecornea, the iris, and the IOL, may be predicted. Further, the anteriorcorneal radius may be measured/simulated. Specifically, in the simulateddata at step 102 for the experimental design of the present invention,the distance between the iris plane and the IOL was held constant at 0.9millimeters for all cases, and the cornea to iris distance was variedbetween 2.1 millimeters and 4.1 millimeters. Of note, the populationaverage ACD of 3.15 millimeters was used for the TECNIS Lens design.

For example, at step 102, a representation of the corneal topography, inthe form of at least the corneal curvature or curvatures, and the pre-and/or post-operative ACD may be obtained using analytical tools knownto those skilled in the art.

For the data accumulated at step 102, step 104 of method 100 calculatesthe spherical aberration at the iris plane. More particularly, step 104may calculate the spherical aberration for a given range of pupils atthe iris plane, such as at a 5 millimeter and 5.3 millimeter pupil.Table 1 illustrates exemplary results for this step 104 for the designedexperiment of the present invention using OSLO simulation program.

TABLE 1 SA (μm) SA (μm) SA Anterior 5.3 mm 5.0 mm cornea (μm) CornealIris Iris 6 mm pupil ACD (mm) Radius (mm) Pupil Pupil 0.12 3 7 0.1100.087 0.39 3 7 0.351 0.278 0.12 5 7 0.153 0.121 0.39 5 7 0.492 0.3900.12 3 8.5 0.100 0.079 0.39 3 8.5 0.324 0.256 0.12 5 8.5 0.129 0.1020.39 5 8.5 0.421 0.333 0.12 4 7.77 0.119 0.094 0.39 4 7.77 0.387 0.3060.27 3 7.77 0.229 0.181 0.27 5 7.77 0.307 0.243 0.27 4 7 0.283 0.2250.27 4 8.5 0.251 0.199 0.27 4 7.77 0.264 0.209

As illustrated in Table 1, the corneal spherical aberration at a 6millimeter pupil was varied as per the distribution for a typicalcataract population. Likewise, the anterior chamber depth in millimeterswas varied as per the distribution for a typical cataract population.Additionally, the corneal strength, referred to in Table 1 as theAnterior Corneal Radius in Millimeters, was also varied. Table 1illustrates, based on these factors, the calculation of sphericalaberration (in micrometers) at the iris plane at the referenced 5 and5.3 millimeter pupil.

The accumulation and/or simulation of data at step 104 may then beemployed to develop a regression formula at step 106. In particularlypreferred embodiments of the present invention, the regression at step106 may account for at least one of corneal spherical aberration andACD, and may further account for other factors, such as corneal power,for example. The regression may empirically indicate constant values forassociation with each such variable factor accounted for in theregression, and may reflect the empirical and/or simulated findings forthe spherical aberration at the iris plane at step 104.

Step 108 may use the regression calculation of step 106 in a calculationof a customized recommendation of one or more IOL characteristics. Step108 may include, for example, determining a desired postoperativecondition, such as a postoperative refraction and/or sphericalaberration, and calculating IOL characteristics such that the desiredpostoperative condition is achieved. The desired refractive outcome maybe, for example, improved distance vision and/or near vision, such asproviding the patient with sufficient visual acuity to eliminate theneed for external corrective spectacles or contact lenses for nearand/or distant vision.

The expected postoperative conditions may be used to compute the IOLcharacteristics by means, for example, of an analytical tool (e.g., aregression routine) employing the empirical regression outcome from step106, and/or by means of using the empirical outcome of step 106 in asecondary regression. For example, the patient eye may be simulated in aregression step 108 that includes, as a characteristic of the modeledpatient eye, the empirical outcome of spherical aberration at the irisplane gained at step 106. Such a regression may allow for thecalculation of different optical quality parameters from which themodulation transfer function (MTF) can be retrieved. The area under theMTF may then be used to assess whether the desired postoperativecondition(s) is met by the modeled IOL of step 108.

Alternatively, at step 108, a classical regression calculation may bemodified by the regression outcome for spherical aberration at the irisplane derived at step 106. More particularly, using the data from step102, a regression analysis may be performed, based on pre-operative dataand the regression outcome of step 106, to provide the recommended IOLcharacteristics at step 108, such as the optimum IOL power.

Method 100 thus accounts for the non-constant nature of SA and ACD in abroader population of surgical subjects. As such, method 100 isapplicable to average eyes, as that term is defined above, and tonon-average eyes, such as eyes having significant variations from theaverage range in SA and/or ACD.

FIG. 4 is a bar diagram illustrating, based on an execution of method100 using the aforementioned MODDE design of experiments, thesignificance of certain factors in the spherical aberration response atthe iris. That is, FIG. 4 illustrates the importance of particularfactors in a regression formula predicting spherical aberration at theiris plane. The factors included in FIG. 4 are the SA, the ACD, thecorneal strength, the SA crossed with the ACD, the SA crossed with thecorneal strength, and the ACD crossed with the corneal strength.

FIG. 4 illustrates that the corneal SA and the expected post-operativeACD are the most important factors in influencing the residual aphakicspherical aberration at the pupil plane. As such, the design ofexperiments discussed in Table 1, in conjunction with certain of theresults illustrated in FIG. 4, may be used to develop the regression, atstep 106, that is predictive of the aphakic spherical aberration at thepupil plane. That regression equation, including the factors referencedabove, namely the corneal power, the SA, the expected post-operativeACD, and the cross terms, is:

SA_(r)=−0.285451+1.00614*SA_(c)+0.0742716*ACD+0.0371122*cor+0.153398*SA_(c)*ACD−0.0788237*SA_(c)*cor−0.00967978*cor*ACD  [EQUATION1]

where SA_(r) is the spherical aberration at the iris plane, SA_(c) isthe corneal SA, and cor is the anterior corneal radius.

FIG. 5 is a graphical illustration of the predicted aphakic sphericalaberration at the iris plane for a pupil of 5.3 millimeters and ananterior corneal radius of 7 millimeters. More particularly, FIG. 5illustrates the outcome of the spherical aberration at the iris planefor the association of the constants in EQUATION 1 with the variableinputs shown in FIG. 5.

Similarly, FIG. 6 graphically illustrates the predicted aphakicspherical aberration at the iris plane for a pupil of 5.3 millimetersand an anterior corneal radius of 7.77 millimeters. Of note, the TECNISLens, for example, is designed for a SA of 0.27 micrometers and an ACDof 4 millimeters. Thus, the design parameters from EQUATION 1 mayprovide, such as in the exemplary embodiment shown in FIG. 6, a lenscustomized to address spherical aberration at the iris plane over asignificantly greater percentage of population variations, in SA andACD, than is provided by the prior art.

FIG. 7 illustrates the predicted aphakic spherical aberration at theiris plane for a pupil of 5.3 millimeters and an anterior corneal radiusof 8.5 millimeters. FIG. 7 again illustrates the accounting, by EQUATION1, for a number of factors affecting the spherical aberration at theiris plane not accounted for in prior art methods.

FIGS. 5 through 7 illustrate that an IOL design for the averagepopulation, with respect to at least SA and ACD, is unlikely to providethe expected visual outcome over a population of patients havingsignificant variations from the average SA and ACD. This undesirableoutcome occurs because prior lens designs cannot drive post-operativespherical aberration at the iris plane to 0 or near 0, due at least tothe dependency of post-operative spherical aberration at the iris planeon the pre-operative SA and the post-operative ACD. More particularly,spherical aberration at the iris plane cannot be driven towards 0 ornear 0 for patients having SA and ACD outside the average using theprior art solutions, because prior art lens designs account only for theaverage data with respect to these variables.

Thus, unlike the prior art, method 100 provides customized treatment foreyes matching different, non-average eye model parameters. For example,in accordance with EQUATION 1, eyes with a large ACD typically correlatenegatively with corneal radius. The present invention has applied IOLsdesigned using method 100 to three customized eye models, namely theTECNIS lens eye model for the average eye, an eye having a large iris tocornea distance, a high corneal spherical aberration and a high cornealpower, and an eye having a small iris to cornea distance, a lowspherical aberration and a low corneal power.

Table 2 provides the inputs for the design of three IOLs, using thevariables listed including the TECNIS lens design. The IOL designscompensate fully for the spherical aberration. Of course, it goeswithout saying that other subdivisions and combinations of variableinputs may be used for lens designs using equation 1 which output theaphakic spherical aberration at the pupil plane ranging from 0.079 μm to0.390 μm for 5 mm pupil for the variables listed. These outputs may beused to design IOLs with a SA to optimize ocular SA outcomes. Using theresidual SA at the pupil plane or predicted IOL plane, an optimal SAvalue of the IOL may be designed and selected to obtain the targetedocular SA.

TABLE 2 Corneal Anterior spherical IOL Corneal Cornea-iris aberration 6mm Conical Design radius (mm) Distance (mm) pupil (μm) constant L_L 8.52.1 0.12 −0.4 TECNIS 7.77 3.1 0.27 −0.18 H_H 7 4.1 0.39 0

The three exemplary lens designs set forth in Table 2, with 20 dioptersof optical power, were tested using the white light modulation transferfunction (50 c/millimeter) and a plurality of eye models having averagecorneal power (anterior radius of 7.77 millimeters) and a 5 millimeterpupil. In accordance with these tests, the SA and the ACD were varied.The results of this testing are provided in FIGS. 8, 9 and 10, at SA of0.12 micrometers, 0.27 micrometers, and 0.39 micrometers, respectively.The results of FIGS. 8-10 demonstrate that best-focus MTF results may beobtained with the present invention, thus indicating that sphericalaberration at the iris plane may be minimized, for realistic amounts ofACD and SA, across a broader population of eyes than was treatable toobtain best-focus MTF in the prior art.

Of course, and as referenced above, various combinations may beprovided, such as lower or higher corneal power, in combination withother factors, other than those graphically shown in the exemplaryillustrations herein. In such circumstances, EQUATION 1 and method 100still provide improved meeting of expected MTF behavior for the lensunder design, i.e. method 100 better provides the expected improvedvisual results. In light of this expectation of improved visualperformance, a surgeon may, in accordance with the present invention,select an IOL meeting the conditions of step 108 of method 100, whereinthe selected IOL is appropriate for the patient based on an expectedaphakic spherical aberration as indicated by EQUATION 1.

Those skilled in the art will appreciate, in light of the discussionherein, that other criteria may be incorporated to obtain the desiredvisual outcome, and that the present invention may be applied incircumstances of non-typical IOLs and other eye treatments. For example,depth of focus may be included as a criteria for the desired visualoutcome, and may be balanced with a best focus design parameter.Likewise, terms may be included to account for other variables such as,for example, LHP or predicted postoperative vitreous length, otheraberrations, or the like. Further, in addition to typical IOLs, thepresent invention may be employed with multifocal IOLs, basicprocedures, glasses and contact lenses, by way of non-limiting example.

FIG. 11 is a block diagram illustrating the implementation of thepresent invention in a clinical system 300 comprised of one or moreapparatuses that are capable of assessing the eye's biometry and ofperforming the calculations and comparisons set forth in method 100. Thesystem 300 may include a biometric reader and/or biometric simulationinput 301, a processor 302, and a computer readable memory 304 coupledto the processor 302. The computer readable memory 304 includes thereinan array of ordered values 308 and sequences of instructions 310 which,when executed by the processor 302, cause the processor 302 to select animplantable IOL configured for implantation into the eye of the subjectpresenting the biometric readings to biometric reader 301. The array ofordered values 308 may comprise data used or obtained from method 100 orother methods consistent with embodiments of the invention. For example,the array of ordered values 308 may comprise one or more desiredrefractive outcomes, parameters of an eye model based on one or morecharacteristics of at least one eye, and data related to characteristicsof an IOL or set of IOLs, such as optical power, an aspheric profile,and/or a lens plane.

The sequence of instructions 310 may include one or more steps of method100 or other methods consistent with embodiments of the invention. Insome embodiments, the sequence of instructions 310 includes applying thecustom regression of method 100 and EQUATION 1, performing one or morecalculations to determine a predicted refractive outcome based on an eyemodel, a regression algorithm, comparing a predicted refractive outcometo a desired refractive outcome, and based on the comparison, repeatingthe calculation with an IOL having at least one of a different power, adifferent aspheric profile, and a different lens plane.

The processor 302 may be embodied in a general purpose desktop or laptopcomputer, and/or may comprise hardware associated with biometric reader301 specifically for selecting an IOL for placement into the eye of thesubject. In certain embodiments, the system 300 may be configured to beelectronically coupled to another device, such as one or moreinstruments for obtaining measurements of an eye or a plurality of eyesin conjunction with, or in addition to, biometric reader 301.Alternatively, the system 300 may be embodied in a handheld device thatmay be adapted to be electronically and/or wirelessly coupled to one ormore other devices.

Additional studies were conducted to predict ocular sphericalaberration, where simulations were performed using a realistic eyemodel. The eye model exhibits the average corneal SA and chromaticaberration found in a population of cataract patients. Publishedclinical data on variations in corneal geometry and a 2 mm range inintraocular lens position were input into the model. A predictive modelusing different ocular geometry was built from the simulations.

The spherical aberration was calculated in the aphakic eye model at thepupil plane (5.3 mm) varying as follows: anterior corneal radius: 7mm-8.5 mm; corneal SAc 6 mm: 0.12 μm-0.39 μm; Cornea-pupil distance PP:2.1 mm-4.1 mm. PP is equal to the ACD as defined before minus 0.9 mm.

The simulations resulted in a quadratic predictive model, with a highdegree of correlation (R2=0.96) showing that the propagated SA stronglydepends on corneal SAc and position of pupil plane, but not on cornealpower. FIG. 12 illustrates the dependence of propagated sphericalaberration with corneal spherical aberration (6 mm) and pupil plane. Theregression equation for SA at the pupil plane is:

SA=0.054833−0.02816*PP+0.004457PP²+0.395401*Sac+0.274583*SAc²+0.152815*PP*SAc  [EQUATION2]

The prediction of true lens position and measured postoperative cornealspherical aberration was used to calculate the ocular sphericalaberration using model illustrated in previous figure above. The truelens position is defined at the position of the posterior vertex of theIOL. The distance PP may now be calculated from the true lens positionby adding the center thickness of IOL and 0.9 mm.

The correlation between calculated and measured ocular sphericalaberration didn't improve when the measured true lens position wasintroduced. The calculated ocular spherical aberration is the predictedvalue from the formula added with the SA of the IOL. See FIG. 13.

Those of ordinary skill in the art may recognize that many modificationsand variations of the present invention may be implemented withoutdeparting from the spirit or scope of the invention. Thus, it isintended that the present invention covers the modifications andvariations of this invention provided they come within the scope of thediscussion herein and any appended claims, and any equivalents thereto.

1-11. (canceled)
 12. A system for predicting at least one characteristicof an intraocular lens, comprising: a first computing device capable ofmeasuring at least one biometric parameter of an eye; a second computingdevice programmed to simulate a corneal spherical aberration and apost-operative anterior chamber depth of the eye according to the atleast one biometric parameter; a third computing device programmed toapply, by at least one computing processor, a regression to the at leastone biometric parameter, the corneal spherical aberration, thepost-operative anterior chamber depth, and cross products thereof,wherein the regression is of the form:SA_(r)=−0.285451+1.00614*SA_(c)+0.0742716*ACD+0.0371122*cor+0.153398*SA_(c)*ACD−0.0788237*SA_(c)*cor−0.00967978*cor*ACD,wherein SA_(r) is spherical aberration at an iris plane of the eye,SA_(c) is the corneal spherical aberration, ACD is the post-operativeanterior chamber depth, and cor is an anterior corneal radius of theeye; and an output from said third computing device, comprising anoptimized one of the at least one characteristic to obtain a desiredpostoperative condition calculated in accordance with the regression.13. The system of claim 12, further comprising a feedback input to saidthird computing device for modifying the regression in accordance withthe optimized one of the at least one characteristic.
 14. The system ofclaim 12, wherein the at least one biometric parameter comprises atleast one of axial length and corneal power preoperative ACD, andpreoperative lens thickness.
 15. The system of claim 12, wherein thedesired postoperative condition comprises a postoperative ocular SA. 16.The system of claim 12, wherein said second device comprises at least acorneal topography simulator which is able to retrieve corneal SA. 17.The system of claim 12, wherein said second device comprises at least aray tracer.
 18. An intraocular lens for association with an eye,comprising: a selected optic from a plurality of available optics,wherein the selected optic comprises a selection capable of correcting aspherical aberration at an iris plane of the eye that obeys theequation:SA_(r) =−A+B*SA_(c) +C*ACD+D*cor+E*SA_(c)*ACD−F*SA_(c)*cor−G*cor*ACD,wherein A, B, C, D, E, F and G are empirically derived constants, SA_(r)is the spherical aberration at the iris plane, SA_(c) is cornealspherical aberration of the eye, ACD is a post-operative anteriorchamber depth of the eye, and cor is an anterior corneal radius of theeye.
 19. The intraocular lens of claim 18, wherein the constant A isabout 0.285451, the constant B is about 1.00614, the constant C is about0.0742716, the constant D is about 0.0371122, the constant E is about0.153398, the constant F is about 0.0788237, and the constant G is about0.00967978.
 20. An intraocular lens for association with an eye,comprising: a selected optic from a plurality of available optics,wherein the selected optic comprises a selection capable of correcting aspherical aberration at an iris plane of the eye that obeys theequation:SA_(pp) =+A−B*PP+C*PP² +D*SA_(c) +E*SA_(c) ² +F*PP*SA_(c) wherein A, B,C, D, E, and F are empirically derived constants, SA_(pp) is thespherical aberration at the pupil plane, PP is the pupil plane, and SAGis corneal spherical aberration of the eye.
 21. The intraocular lens ofclaim 20, wherein the constant A is about 0.054833, the constant B isabout 0.02816, the constant C is about 0.004457, the constant D is about0.395401, the constant E is about 0.274583, and the constant F is about0.152815.